Analysis for Time Discrete Approximations of Blow-up Solutions of Semilinear Parabolic Equations

Irene Kyza, Charalambos Makridakis

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    13 Citations (Scopus)

    Abstract

    We prove a posteriori error estimates for time discrete approximations, for semilinear parabolic equations with solutions that might blow up in finite time. In particular we consider the backward Euler and the Crank-Nicolson methods. The main tools that are used in the analysis are the reconstruction technique and energy methods combined with appropriate fixed point arguments. The final estimates we derive are conditional and lead to error control near the blow up time.

    Original languageEnglish
    Pages (from-to)405-426
    Number of pages22
    JournalSIAM Journal on Numerical Analysis
    Volume49
    Issue number1
    DOIs
    Publication statusPublished - 2011

    Keywords

    • energy techniques
    • CRANK-NICOLSON METHOD
    • Crank-Nicolson method
    • POSTERIORI ERROR ANALYSIS
    • BEHAVIOR
    • blow-up solutions and rate
    • conditional a posteriori estimates
    • backward Euler method
    • NONLINEAR HEAT-EQUATIONS
    • MEAN-CURVATURE
    • reconstruction technique
    • semilinear parabolic equations
    • Duhamel's principle
    • fixed point arguments

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